Question

A circle's center is at `(8 ,1 )` and it passes through `(2 ,5 )`. What is the length of an arc covering `(5 pi ) /6` radians on the circle?

Answer 1

(8,1) and (2,5)

`d^2=(8-2)^2+(1-5)^2`

`d^2=36+16`

`d=sqrt 52`

The distance between the points is `sqrt53` so the radius of the circle is `sqrt52`

Length of an arc is `theta/360xxpiD`

Where `theta` is the angle of the arc and `D` is the diameter of the circle.

`[5pi]/6=150^@`

Length=`150/360xxpixx2sqrt52`

Length is 18.87862233